Question

4. The circumference of a circle is 1232 cm
Calculate
c) the radius of the circle in om
c) the area of the circle to the nearest om?
Od the effect on the area of the circle of the radio i doubled.​

Answer 1

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✦ Correct Question:-

4)The circumference of a circle is 1232 cm

☘Calculate

a) the radius of the circle in cm

b) the area of the circle to the nearest cm^2?

Find the effect on the area of the circle of the radius is doubled.

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✦ Required Answer:-

♦️ GiveN:

• Circumference/perimeter of the circle = 1232 cm

♦️ To FinD:

• Radius
• Area of circle
• Effect on area when radius is doubled

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✦ How to Solve?

The above is very simple, just apply formula and get solution type question. We just need to know the basic formulae like perimeter of circle, area of circle.

Here, r = radius of the circle

$\large{\boxed{\red{\rm{Perimeter \:of \:circle = 2\pi r}}}}$

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$\large{\boxed{\red{\rm{Area\:of \:circle =\pi {r}^{2}}}}}$

By using these formula, let's solve this question.

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✦Solution:

(i)Given, Circumference = 1232 cm

So, we can find the radius of the circle, as we know the circumference and value of pi.

By using formula,

$\large{ \rm{ \longrightarrow \: 2\pi r = 1232 \: cm}} \\ \\ \large{ \rm{ \longrightarrow \: 2 \times \frac{22}{7} \times r = 1232 \: cm}} \\ \\ \large{ \rm{ \longrightarrow \: r = \cancel{\frac{1232 \times 7}{2 \times 22} \: cm}}} \\ \\ \large{ \rm{ \longrightarrow \: r = \boxed{ \rm{ \green{196 \: cm}}}}}$

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(ii) Now as we have got our radius, let's find out the area of circle by applying formula,

By using formula,

$\large{ \rm{ \longrightarrow \: Area \: of \: circle = \pi {r}^{2}}} \\ \\ \large{ \rm{ \longrightarrow \: Area \: of \: circle = \pi(196) {}^{2} \: {cm}^{2} }} \\ \\ \large{ \rm{ \longrightarrow \: Area \: of \: circle = \frac{22}{7} \times 196 \times 196 \: {cm}^{2} }} \\ \\ \large{ \rm{ \longrightarrow \: Area \: of \: circle = 22 \times 28 \times 196 \: {cm}^{2}}} \\ \\ \large{ \rm{ \longrightarrow \: Area \: of \: circle = \boxed{ \rm{ \green{120736 \: {cm}^{2} }}}}}$

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Let our original radius be r

$\large{ \rm{ \longrightarrow \: Area \: of \: circle = \pi {r}^{2}}}$

And, final radius = 2r (Radius getting doubled)

$\large{ \rm{ \longrightarrow \: New \: area \: of \: circle = \pi(2r) {}^{2} }} \\ \\ \large{ \rm{ \longrightarrow \: New \: area \: of \: circle = 4\pi {r}^{2}}}$

So, Area becomes 4 times of the original, Although you have not mentioned, Still I am finding the % change.

% change in area,

$\Large{ \rm{ \longrightarrow \frac{New \: area - Original \: area}{Original \: area} \times 100}}$

So, by using formula,

$\large{ \rm{ \longrightarrow \: \% \: change \: in \: area = \frac{4\pi {r}^{2} - \pi {r}^{2} }{\pi {r}^{2} } \times 100}} \\ \\ \large{ \rm{ \longrightarrow \: \% \: change \: in \: area = \frac{3\pi {r}^{2} }{\pi {r}^{2} } \times 100\: }} \\ \\ \large{ \rm{ \longrightarrow \: \% \: change \: in \: area = \boxed{ \rm{ \green{300\%}}}}}$

The area increase by 300 % when radius is doubled.

$\large{ \therefore{ \underline{ \underline{ \rm{ \pink{Hence, \: solved \: \dag}}}}}}$

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